The gear generating machining employs the electronic gearbox (EGB) to achieve precise synchronization between the motion axes, and the gear ma-chining accuracy largely depends on the multi-axis control accuracy of the EGB. However, there are still shortcomings in the research on the relation-ship between multi-axis control accuracy and gear machining accuracy, especially in continuous generating grinding. This paper introduces a method for predicting and compensating gear machining errors based on the multi-axis motion control of the EGB, aiming to address the unclear relationship between multi-axis motion control accuracy and gear machining accuracy. A mapping model is derived, connecting the motion errors of the gear grinding machine with profile deviations, helix deviations, and pitch deviations, based on the characteristics of continuous generating grinding and the mechanisms of gear machining errors. Verification through simulations confirms that reducing motion errors can compensate for gear machining errors. The results indicate that the method proposed in this paper offers a feasible solution for improving gear machining accuracy.